Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Auckland to Steamboat Springs as you normally would.
Auckland Intl (AKL) is the airport you will fly out of if you book a flight from Auckland to Steamboat Springs. You should not have trouble finding flights to Steamboat Springs from Auckland Intl; the airport handles an average of 0 outbound flights to Steamboat Springs per day. You should also have plenty of airline options to choose from since 2 airlines have flights from the Auckland airport to Steamboat Springs. It is only a 17.9 km journey to Auckland Intl (AKL) from Auckland’s city centre.